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Since this is a 2nd Edition, we are giving below the topics we wish to add/update/revise in roughly the same chapter sequence as we had in the existing 1st Edition of the book. In addition to a general revision of the text, we propose the following major modifications (the asterisks denote the amount of text added/modified and/or or the difficulty level of the topics being discussed):   Chapter 2   - Subsection 2.1.2: add discussion on how to find all zeros by means   of the Newton method (*)   Chapter 3   - Expand Subsection 3.2.7 on solving the A*x = b equations with sparse   matrices to a full Section (**) - Expand Subsection 3.4.5 on solving the eigenvalue problem A*x = lambda*x   to a full Section (**) - Discuss the exponentiation of a matrix, exp(A) (*) - Add a Subsection on Pseudospectra (**) - in general, enhance the "sparse" aspect of the chapter   Chapter 4   - Add a new Section on Sparse FFT (following present Sec. 4.2),   add corresponding Exercise (**) - Expand Subsection 4.6.2 on the Discrete Wavelet Transform   to a full Section, add Exercise (***) - Add a Section on image denoising (**) - Add Section on Radon transformation (**)   Chapter 5   - Rewrite Sections 5.1-5.5 to better distinguish between general   discussion of distributions and the techniques involving samples,   and to bring the notation in line with the book "Probability   for Physicists" (***) - Introduce Bayesian data analysis and inference (***) - Expand Subsection 5.5.8 on Non-linear Regression to a full Section,   add Exercises (**)   Chapter 6   - Expand Section 6.5 on Noise, add Exercise (**) - Add Section on Takens Theorem and its applications: phase space   reconstruction and optimal size determination (**) - Add discussion on signal entropies (**) - Update discussion on autoregressive models (optimal order) (*) - Add discussion on signal directionality / causality (**)   Chapter 7   - Expand Section 7.10 on Stiff Problems of ODE, add Exercise (**)   Chapter 8   - Expand Subsection 8.7.4 on Singular SL Problems to a Section,   add Exercise (**) - Motivated by Section 8.8, write a new chapter on Inverse Problems (***)   Chapter 10   - Expand Section 10.8, add Exercise (**)   Chapter 11   - Expand Sections 11.7 and 11.8, add Exercises (**)   New Chapter on Inverse Methods (***)   New short Chapter or Appendix on minimization (**) - with derivatives or without them - with constraints or without them - deterministic and quasi-deterministic (MC methods)   New Appendix on spline methods: B-splines, Bezier splines (**)